The field of the invention is digital signal filtering and in particular methods to improve low frequency resolution without increasing processing requirements.
Broadband digital signals often require filtering for their intended use. For example, in audio systems, signals may be filtered (often referred to as equalizing) to compensate for characteristics of speakers and the listening environment. Such digital signals must be at a sufficiently high sample rate to carry the high frequency signal components. Finite Impulse Response (FIR) (or transversal) filters are preferred in many applications to maintain linear phase or minimum phase for accurate sound reproduction. In order to filter such signals using a single FIR filter, the filtering must be performed at the high sample rate of the digital signal, and to achieve high resolution filtering for low frequencies present in the signal, a very long FIR filter is also required. In some audio systems the resulting processing requirements cannot be performed economically.
Multi-rate filters have been introduced to overcome the very long FIR filter requirement of single filter implementations. Such multi-rate filters separate the digital signal into at least two bands. A high frequency signal band is processed at the high sample rate of the original signal using a short FIR filter and a parallel low frequency band is first down sampled to a lower sample rate, filtered using a FIR filter which may be much shorter than the traditional filter required by the single filter implementation, and up sampled back to the original sample rate. The two filtered signals are then summed to provide the desired filtered signal. Such multi-rate filters include a high pass filter to provide the high frequency signal, and a separate low pass filter to provide the separate parallel low frequency signal. While Infinite Impulse Response (IIR) high pass and low pass filters might be used in the multi-rate filter, but unfortunately such IIR filters introduce differing group delay above and below the transition frequency and may distort the resulting audio signal. Alternatively, linear phase FIR's may be used, but unfortunately the FIR high and low pass filters are computationally intense, and minimize the benefit of the multi-rate filtering approach.